where \(\widetilde{\Gamma }^{\lambda }_{\;\;\;\mu \nu }\)  is the usual Levi-Civita connection calculated only by the metric and its first derivatives. Once the distortion is given, torsion and non-metricity can be quite easily computed through (see for instance [1]})
\(S_{\mu \nu \alpha }=N_{\alpha [\mu \nu ]}\;\;,\;\;\; Q_{\nu \alpha \mu }=2 N_{(\alpha \mu )\nu } \) 
